You are charged $16.05 for a meal. Assume sales tax is 7%, what was the menu price for the meal?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Problem Statement:
You are charged $16.05 for a meal. Assume sales tax is 7%, what was the menu price for the meal?

### Explanation:
To determine the original menu price of the meal before the sales tax was added:

1. **Understand the problem**: We need to find the original price before adding a 7% sales tax. The total amount charged after adding the tax is $16.05.
   
2. **Formula**: 
   \[
   \text{Total Price} = \text{Menu Price} + (\text{Menu Price} \times \text{Sales Tax Rate})
   \]

   In this problem, we know the Total Price is $16.05 and the Sales Tax Rate is 7% (or 0.07).

3. **Rewriting the formula**:
   \[
   \text{Total Price} = \text{Menu Price} \times (1 + \text{Sales Tax Rate})
   \]
   \[
   16.05 = \text{Menu Price} \times 1.07
   \]

4. **Solving for Menu Price**:
   \[
   \text{Menu Price} = \frac{\text{Total Price}}{1 + \text{Sales Tax Rate}}
   \]
   \[
   \text{Menu Price} = \frac{16.05}{1.07}
   \]
   \[
   \text{Menu Price} = 15
   \]

### Answer:
The menu price for the meal before tax was $15.00.

**Diagram/Graph Explanation**:
There are no graphs or diagrams in the provided image. The box appears to be a place for students to enter their answer after calculating the menu price.
Transcribed Image Text:### Problem Statement: You are charged $16.05 for a meal. Assume sales tax is 7%, what was the menu price for the meal? ### Explanation: To determine the original menu price of the meal before the sales tax was added: 1. **Understand the problem**: We need to find the original price before adding a 7% sales tax. The total amount charged after adding the tax is $16.05. 2. **Formula**: \[ \text{Total Price} = \text{Menu Price} + (\text{Menu Price} \times \text{Sales Tax Rate}) \] In this problem, we know the Total Price is $16.05 and the Sales Tax Rate is 7% (or 0.07). 3. **Rewriting the formula**: \[ \text{Total Price} = \text{Menu Price} \times (1 + \text{Sales Tax Rate}) \] \[ 16.05 = \text{Menu Price} \times 1.07 \] 4. **Solving for Menu Price**: \[ \text{Menu Price} = \frac{\text{Total Price}}{1 + \text{Sales Tax Rate}} \] \[ \text{Menu Price} = \frac{16.05}{1.07} \] \[ \text{Menu Price} = 15 \] ### Answer: The menu price for the meal before tax was $15.00. **Diagram/Graph Explanation**: There are no graphs or diagrams in the provided image. The box appears to be a place for students to enter their answer after calculating the menu price.
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